Vol. 11, No. 8, 2017

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Torsion orders of complete intersections

Andre Chatzistamatiou and Marc Levine

Vol. 11 (2017), No. 8, 1779–1835
Abstract

By a classical method due to Roitman, a complete intersection X of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer N, when viewed as a cycle in the Chow group, has support in X × D F × X, for some divisor D and a finite set of closed points F. The minimal such N is called the torsion order. We study lower bounds for the torsion order following the specialization method of Voisin, Colliot-Thélène, and Pirutka. We give a lower bound for the generic complete intersection with and without point. Moreover, we use methods of Kollár and Totaro to exhibit lower bounds for the very general complete intersection.

Keywords
algebraic cycles, decomposition of the diagonal
Mathematical Subject Classification 2010
Primary: 14C25
Milestones
Received: 23 May 2016
Revised: 14 June 2017
Accepted: 29 July 2017
Published: 15 October 2017
Authors
Andre Chatzistamatiou
Fakultät Mathematik
Universität Duisburg-Essen
Essen
Germany
Marc Levine
Fakultät Mathematik
Universität Duisburg-Essen
Essen
Germany